Installed new kitchen sink, but no water?

First time poster! I just removed, and installed a new kitchen sink. The sink is a white cast iron American Standard, two basin sink. The faucet is a Kohler, single lever with a sprayer & a soap pump.

All went well until I turned the supply valves on to furnish water [ressure -but nothing.

The water supply lines H & C, come out of the wall, then into what I guess would be called a 2 way or 3 way valve. The Hot has a hand valve for the supply going up to the sink, then another which goes to the dishwasher. The cold has a H/V which supplies pressure to the facuet, then another H/V which supllies the line going to the ice maker.

This is the first time, to my knowledge that this job has been done. I believe the condo unit to be approxiamtely 20 years old.

Other than the 2way or three way valves is there anything else I should check out? I did cycle all of the hand valves 4 - 5 times, with the same result.

if you unscrew the aerator on the spout and turn on the faucet what happens? unhook the supply lines from the faucet and turn on the water, with the supply running into a bucket, to see if you have pressure.

Try loosening the top of the lever and moving the part underneath to the right or left. the position of this part determines which way the water comes out.... hot - righ or left, cold - right or left, or no water at all.

I recently did the exact same job and had the exact same result.
When I remodeled my kitchen and installed a new sink and faucet set, I could not get any cold water. Apparently when I was wrestling with the pipes I jarred some sediment loose and it blocked the new shut-off valve. I disassebled my work (removed the shut off valve to where I had a direct 1/2 line coming out from under the cabinet), had my wife to hold a 5 gallon bucket as close as possible to the pipe, went outside turned on the water and turned it off as quick as possible. I then checked to make sure there was no sediment in the shut-off valve and cleaned out the faucet diffuser.
Problem solved!

Note* I enjoyed my wife in the wet Tee-shirt...but I don't think she did.

I just wanted to pass along that I resolved the problem. Before removing the sink, I decided to check the hoses and their routing, ine more time. One hose coming out of the faucet, was a Quick Disconnect (QD) type. Since it was easily reachable, I decided to disconnect, then reconnect, and lo & behold - I have water!!!

Apparently, I didn't have the QD pushed in enoought to unseat the poppet, so no water.

Now all I have left is to seal the perimeter if the sink, clean up and enjoy the rest of my Sunday.

Thanks for all your advice, you saved me the expens of alling in a pro, not to mention a few bucks!!